1. Field of the Invention
The present invention relates generally to a channel encoding/decoding apparatus and method, and in particular, to a channel encoding/decoding apparatus and method using a parallel concatenated low density parity check codes.
2. Description of the Related Art
With the rapid progress of a mobile communication system, technology for transmitting a large volume of data at and up to a capacity level presently available in wired networks must be developed for a wireless network. As a high-speed, high-capacity communication system capable of processing and transmitting various information such as image data and radio data as well as simple voice service data is required, it is necessary to increase the system transmission efficiency using an appropriate channel coding scheme in order to improve the system performance. However, a mobile communication system inevitably experiences errors occurring due to noise, interference and fading according to channel conditions during data transmission. The occurrence of errors causes a loss of information data.
In order to reduce the information data loss due to the occurrence of errors, it is possible to improve reliability of the mobile communication system by using various error-control schemes. The most popularly used error-control scheme uses an error-correcting code. A description will now be made of a turbo code and a low density parity check (LDPC) code, which are typical error correcting codes.
A. Turbo Code
It is well known that the turbo code is superior in performance gain to a convolutional code conventionally used for error correction, during high-speed data transmission. The turbo code is advantageous in that it can efficiently correct an error caused by noises generated in a transmission channel, thereby increasing the reliability of the data transmission.
B. LDPC Code
The LDPC code can be decoded using an iterative decoding algorithm based on a sum-product algorithm on a factor graph. Because a decoder for the LDPC code uses the sum-product algorithm-based iterative decoding algorithm, it is lower in complexity to a decoder for the turbo code. In addition, the decoder for the LDPC code is easy to implement with a parallel processing decoder, compared with the decoder for the turbo code.
Shannon's channel coding theorem shows that reliable communication is possible only at a data rate not exceeding a channel capacity. However, Shannon's channel coding theorem has proposed no detailed channel encoding/decoding method for supporting a data rate up to the maximum channel capacity limit. Generally, although a random code having a very large block size shows performance approximating a channel capacity limit of Shannon's channel coding theorem, when a MAP (Maximum A Posteriori) or ML (Maximum Likelihood) decoding scheme is used, it is actually impossible to implement the decoding scheme because of its heavy calculation load.
The turbo code was proposed by Berrou, Glavieux and Thitimajshima in 1993, and has superior performance approximating a channel capacity limit of Shannon's channel coding theorem. The proposal of the turbo code triggered active research on iterative decoding and graphical expression of codes, and LDPC codes proposed by Gallager in 1962 have been newly spotlighted in the research. Cycles exist on a factor graph of the turbo code and the LDPC code, and it is well known that iterative decoding on the factor graph of the LDPC code where cycles exist is suboptimal. Also, it has been experimentally proven that the LDPC code has excellent performance through iterative decoding. The LDPC code known to have the highest performance ever shows performance having a difference of only about 0.04 [dB] at a channel capacity limit of Shannon's channel coding theorem at a bit error rate (BER) 10−5, using a block size 107. In addition, although an LDPC code defined in Galois Field (GF) with q>2, i.e., GF(q), increases in complexity in its decoding process, it is much superior in performance to a binary code. However, there has been provided no satisfactory theoretical description of successful decoding by an iterative decoding algorithm for the LDPC code defined in GF(q).
The LDPC code, proposed by Gallager, is defined by a parity check matrix in which major elements have a value of 0 and minor elements except the elements having the value of 0 have a value of non-0, e.g., 1. For example, an (N, j, k) LDPC code is a linear block code having a block length N, and is defined by a sparse parity check matrix in which each column has j elements having a value of 1, each row has k elements having a value of 1, and all of the elements except for the elements having the value of 1 all have a value of 0.
An LDPC code in which a weight of each column in the parity check matrix is fixed to ‘j’ and a weight of each row in the parity check matrix is fixed to ‘k’ as stated above, is called a “regular LDPC code.” Herein, the “weight” refers to the number of elements having a non-zero value among the elements constituting the generating matrix and parity check matrix. Unlike the regular LDPC code, an LDPC code in which the weight of each column in the parity check matrix or the weight of each row in the parity check matrix are not fixed is called an “irregular LDPC code.” It is generally known that the irregular LDPC code is superior in performance to the regular LDPC code. However, in the case of the irregular LDPC code, because the weight of each column or the weight of each row in the parity check matrix are not fixed, i.e., are irregular, the weight of each column in the parity check matrix or the weight of each row in the parity check matrix must be properly adjusted in order to guarantee the superior performance.
With reference to FIG. 1, a description will now be made of a parity check matrix of an (8, 2, 4) LDPC code as an example of an (N, j, k) LDPC code.
FIG. 1 is a diagram illustrating a parity check matrix of a general (8, 2, 4) LDPC code. Referring to FIG. 1, a parity check matrix H of the (8, 2, 4) LDPC code is comprised of 8 columns and 4 rows, wherein a weight of each column is fixed to 2 and a weight of each row is fixed to 4. Because the weight of each column and the weight of each row in the parity check matrix are regular as stated above, the (8, 2, 4) LDPC code illustrated in FIG. 1 becomes a regular LDPC code.
FIG. 2 is a diagram illustrating a factor graph of the (8, 2, 4) LDPC code of FIG. 1. Referring to FIG. 2, a factor graph of the (8, 2, 4) LDPC code is comprised of 8 variable nodes of x1 211, x2 213, x3 215, x4 217, x5 219, x6 221, x7 223 and x8 225, and 4 check nodes 227, 229, 231 and 233. When an element having a value of 1, i.e., a non-zero value, exists at a point where an ith row and a jth column of the parity check matrix of the (8, 2, 4) LDPC code cross each other, a branch is created between a variable node xi and a jth check node.
Because the parity check matrix of the LDPC code has a very small weight as described above, it is possible to perform decoding through iterative decoding even in a block code having a relatively long length, that exhibits performance approximating a capacity limit of a Shannon channel, such as a turbo code, while continuously increasing a block length of the block code. MacKay and Neal have proven that an iterative decoding process of an LDPC code using a flow transfer scheme is approximate to an iterative decoding process of a turbo code in performance.
In order to generate a high-performance LDPC code, the following conditions should be satisfied.
(1) Cycles on a Factor Graph of an LDPC Code Should be Considered.
The term “cycle” refers to a loop formed by the edges connecting the variable nodes to the check nodes in a factor graph of an LDPC code, and a length of the cycle is defined as the number of edges constituting the loop. A cycle being long in length means that the number of edges connecting the variable nodes to the check nodes constituting the loop in the factor graph of the LDPC code is large. In contrast, a cycle being short in length means that the number of edges connecting the variable nodes to the check nodes constituting the loop in the factor graph of the LDPC code is small.
As cycles in the factor graph of the LDPC code become longer, the performance efficiency of the LDPC code increases, for the following reasons. That is, when long cycles are generated in the factor graph of the LDPC code, it is possible to prevent performance degradation such as an error floor occurring when too many cycles with a short length exist on the factor graph of the LDPC code.
(2) Efficient Encoding of an LDPC Code Should be Considered.
It is difficult for the LDPC code to undergo real-time encoding compared with a convolutional code or a turbo code because of its high encoding complexity. In order to reduce the encoding complexity of the LDPC code, a Repeat Accumulate (RA) code has been proposed. However, the RA code also has a limitation in reducing the encoding complexity of the LDPC code. Therefore, efficient encoding of the LDPC code should be considered.
(3) Degree Distribution on a Factor Graph of an LDPC Code Should be Considered.
Generally, an irregular LDPC code is superior in performance to a regular LDPC code, because a factor graph of the irregular LDPC code has various degrees. The term “degree” refers to the number of edges connected to the variable nodes and the check nodes in the factor graph of the LDPC code. Further, the phrase “degree distribution” on a factor graph of an LDPC code refers to a ratio of the number of nodes having a particular degree to the total number of nodes. It has been proved by Richardson that an LDPC code having a particular degree distribution is superior in performance.
As described above, it is well known that the LDPC code, together with the turbo code, is superior in a performance gain for high-speed data transmission, and the LDPC code is advantageous in that it can efficiently correct errors caused by noises generated in a transmission channel, thereby increasing the reliability of the data transmission. However, the LDPC code is inferior in a point of view of code rate. That is, because the LDPC code has a relatively high code rate, it is not free from the point of view of the code rate. Conventionally, the LDPC code is only generated in high code rate because of a character of the LDPC code. It is difficult to generate a LDPC code with a relatively low code rate, so the LDPC code is not free from the point of view of the code rate.
In the case of current LDPC codes, most have a code rate of 1/2 and only some have a code rate of 1/3. The limitation in code rate exerts a fatal influence on high-speed, high-capacity data communication. Of course, although a degree distribution representing the best performance can be calculated using a density evolution technique in order to implement a relatively low code rate for the LDPC code, it is difficult to implement an LDPC code having a degree distribution representing the best performance due to various restrictions, such as a cycle structure on a factor graph and hardware implementation.
As mobile communication systems develop, various transmission schemes such as a Hybrid Automatic Retransmission Request (HARQ) scheme and an Adaptive Modulation and Coding (AMC) scheme are used to increase efficiency of resources. A description will now be made of the HARQ scheme and the AMC scheme.
A communication system employing the HARQ scheme must create codes having various code rates using one component code. That is, the HARQ scheme increases its efficiency using a soft combining scheme. The soft combining scheme is classified into a Chase Combining (CC) scheme and an Incremental Redundancy (IR) scheme. In the CC scheme, a transmission side uses the same data for both initial transmission and retransmission. That is, in the CC scheme, if m symbols were transmitted as one coded block at the initial transmission, the same m symbols are transmitted as one coded block even at retransmission. The term “coded block” refers to user data transmitted for one transmission time interval (TTI). That is, in the CC scheme, the same code rate is used for both the initial transmission and retransmission. Then, a reception side soft-combines an initially-transmitted coded block with the retransmitted coded block, and performs a Cyclic Redundancy Check (CRC) operation on the soft-combined coded block to determine whether there is an error in the soft-combined coded block.
In the IR scheme, however, a transmission side uses data in different formats for the initial transmission and retransmission. For example, if n-bit user data is channel-coded into m symbols, the transmission side transmits only some of the m symbols at the initial transmission, and sequentially transmits the remaining symbols at retransmission. That is, in the IR scheme, different code rates are used for the initial transmission and retransmission. Then, a reception side configures coded blocks having a high code rate by concatenating retransmitted coded blocks to the end of the initially-transmitted coded bocks, and then performs error correction. In IR, a coded block transmitted at the initial transmission and coded blocks transmitted at the retransmission are identified by their version numbers. For example, a coded block re-transmitted at initial transmission is assigned a version number #1, a coded block transmitted at first transmission is assigned a version number #2, and a coded block transmitted at second retransmission is assigned a version number #3, and the reception side can soft-combine the initially-transmitted coded block with the retransmitted coded block using the version numbers.
The AMC scheme adaptively selects a modulation scheme and a coding scheme used for each channel according to a channel response characteristic of each channel. The term “coding scheme” refers to a scheme for selecting, for example, a code rate. The AMC scheme has a plurality of modulation schemes and a plurality of coding schemes, and modulates and codes a signal by combining the modulation schemes and the coding schemes. Commonly, combinations of the modulation schemes and the coding schemes are called “Modulation and Coding Scheme (MCS),” and can be defined into a plurality of MCSs with level #1 to level #N. That is, the AMC scheme adaptively selects a level of MCS according to a channel response characteristic between a transmission side, or a Base Station (BS), and a reception side, or a Subscriber Station (SS), thereby improving system efficiency.
As described above, when the HARQ and AMC schemes are used, it is necessary to support various code rates. However, because the LDPC code has limitations in terms of code rate as described above, it is hard to use the HARQ and AMC schemes for the LDPC code. Thus, there is a demand for a channel encoding/decoding scheme capable of supporting various code rates using the LDPC code.